Dad’s Hamburger Sandwich

Preparation

1. Pickled onion

   Step 1

   Cook garlic, bay leaf, peppercorns, and red pepper flakes in a dry small saucepan over medium-high heat, stirring often, until garlic is browned in spots and spices are lightly toasted and fragrant, about 2 minutes. Add vinegar and sugar and bring to a boil. Cook, stirring, until sugar is dissolved, about 1 minute. Remove from heat and let sit 10 minutes.

   Step 2

   Place red onion in an airtight container; strain pickling liquid over. Cover and chill at least 1 hour.

   Do ahead: Onion can be pickled 1 week ahead. Keep chilled.

2. Sauce and assembly

   Step 3

   Whisk together egg yolk, mustard, Worcestershire sauce, vinegar, honey, 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, and 1 tsp. pepper in a medium bowl. Slowly stream in oil, whisking until sauce is emulsified and lightened in color. (Alternatively, you can process in a food processor.) Set aside.

   Step 4

   Heat 2 tsp. ghee in a large skillet over medium-high. Working in batches and adding more ghee between batches if needed, cook bread, undisturbed, until golden brown and crisp underneath, about 3 minutes. Transfer, toasted side down, to a wire rack. Reserve skillet.

   Step 5

   Portion beef into 4 loosely packed balls (4 oz. each); season generously with salt and pepper on all sides.

   Step 6

   Heat remaining 2 Tbsp. ghee in reserved skillet over medium-high. Place balls of meat in skillet and tilt skillet so ghee pools in pan; spoon melted ghee over meat to coat. Using a sturdy metal spatula, press down on meat to form ½"-thick patties. Cook until browned and crisp underneath, about 2 minutes. Flip patties; top patties with cheese. Partially cover skillet and cook until cheese is melted and patties are browned on other side and cooked to desired doneness, about 3 minutes. Transfer to a plate, leaving fat behind.

   Step 7

   Crack eggs into same skillet and cook, shaking pan occasionally to prevent eggs from sticking together, until whites are set but yolks are still runny, about 3 minutes.

   Step 8

   To build sandwiches, spread untoasted side of bread slices with reserved sauce. Arrange a few lettuce leaves over 4 slices, then top each with some drained pickled onion, a patty, and an egg. Close up sandwiches.

   Do ahead: Sauce can be made 3 days ahead. Cover and chill.

   *Raw egg is not recommended for infants, the elderly, pregnant women, people with weakened immune systems…or people who don’t like raw eggs.